This invention relates to a digital filter of a recursive type.
A digital filter comprises digital circuit elements, such as a shift register, a digital multiplier, and a digital adder, and has an excellent frequency characteristic as compared with an analog filter. Inasmuch as the digital circuit elements are readily realized by an integrated circuit, it is possible to render a digital filter compct and inexpensive.
For application to such a digital filter, an analog signal is converted to an input digital signal by sampling the analog signal at a sampling interval or period into analog samples and encoding each analog sample at a clock period or bit interval into a sequence of binary pulses. An input digital signal thus comprises successive input data words, each consisting of binary pulses of a predetermined number of bits or a fixed word length. The digital filter subjects each input data word to a digital operation defined by a filter characteristic to produce an output data word.
Digital filters are broadly classified into those of a recursive and a non-recursive type according as the filter comprises a feedback loop and does not, respectively. A typical non-recursive digital filter is described in U.S. Pat. No. 3,521,041 issued to Richard van Blerkom et al. A non-recursive digital filter is advantageous in that the absence of a feedback loop never results in oscillation due to overflow which will be discussed in detail hereunder. It is, however, difficult with a non-recursive digital filter to implement a desired filter characteristic. On the other hand, a recursive digital filter is exemplified as a recursive second-order filter section in FIG. 2 of an article contributed by Stanley L. Freeny to "Proceedings of the IEEE," Volume 63, No. 4 (April, 1975), pages 633-648, under the title of "Special-Purpose Hardware for Digital Filtering." The recursive second-order filter section is important in practice because it is possible to achieve various filter characteristics by cascading or paralleling such sections as pointed out in the Freeny article with reference to FIGS. 3 and 4 thereof. It should, however, be borne in mind that overflow results from an adder accompanying a feedback path. The overflow gives rise to oscillations, known as limit cycles in the art, to adversely affect the filtering function. A circuit for detecting and correcting the overflow is therefore indispensable. An overflow detection or detect and correction or correct circuit is described in the Freeny article with reference to FIGS. 6 and 18 thereof. As seen from the detail shown in this FIG. 18, the prior art circuit comprises a considerable number of circuit elements and is complicated in structure. This has inevitably rendered the recursive digital filters inexpensive.